Which of the following compounds will most readily be dehydrated to give alkene under acidic condition?

\(A \rightarrow B\) The above reaction is of zero order. Half life of this reaction is \(50\,min\). The time taken for the concentration of \(A\) to reduce to one-fourth of its initial value is \(...........\min\)(Nearest integer)

Choose the correct tests with respective observations.
(A) \(\mathrm{CuSO}_4\) (acidified with acetic acid) \(+ \mathrm{K}_4\left[\mathrm{Fe}(\mathrm{CN})_6\right] \rightarrow\) Chocolate brown precipitate.
(B) \(\mathrm{FeCl}_3+\mathrm{K}_4\left[\mathrm{Fe}(\mathrm{CN})_6\right] \rightarrow\) Prussian blue precipitate.
(C) \(\mathrm{ZnCl}_2+\mathrm{K}_4\left[\mathrm{Fe}(\mathrm{CN})_6\right]\), neutralised with \(\mathrm{NH}_4 \mathrm{OH}\) \(\rightarrow\) White or bluish white precipitate.
(D) \(\mathrm{MgCl}_2+\mathrm{K}_4\left[\mathrm{Fe}(\mathrm{CN})_6\right] \rightarrow\) Blue precipitate.
(E) \(\mathrm{BaCl}_2+\mathrm{K}_4\left[\mathrm{Fe}(\mathrm{CN})_6\right]\), neutralised with NaOH \(\rightarrow\) White precipitate.
Choose the correct answer from the options given below :

A sample of \(\mathrm{CaCO}_3\) and \(\mathrm{MgCO}_3\) weighed \(2.21 \mathrm{~g}\) is ignited to constant weight of \(1.152 \mathrm{~g}\). The composition of mixture is _______. (Given molar mass in \(\mathrm{g} \mathrm{mol}^{-1}{CaCO}_3: 100, \mathrm{MgCO}_3: 84)\)

Given below are two statements :

Statement I : H\(_2\)O molecules move from the chamber \(1\) to chamber \(2\).
Statement II : The osmotic pressure of a solution prepared by dissolving \(50\) mg of potassium sulphate (molar mass \(= 174\) g/mol) in \(2\) L of water (at \(27°\)C) is \(0.0107\) bar. (Given : R \(= 0.083\) dm\(^3\) bar K\(^{-1}\) mol\(^{-1}\) and assume complete dissociation of electrolyte)
In the light of the above statements, choose the correct answer from the options given below :

Given below are two statements :
Statement \(I\): Nitration of benzene involves the following step -

Statement \(II\): Use of Lewis base promotes the electrophilic substitution of benzene.
In the light of the above statements, choose the most appropriate answer from the options given below:

The major product of the following reaction is \(\begin{array}{*{20}{c}}
  {OH\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,} \\ 
  {|\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,} \\ 
  {C{H_3}CHC{H_2}C{H_2}N{H_2}} 
\end{array}\) \(\xrightarrow[{triethyla\min e}]{{ethyl\,formate\,\left( {1\,equiv} \right)}}\)

The locus of a point which divides the line segment joining the point \((0,-1)\) and a point on the parabola, \(\mathrm{x}^{2}=4 \mathrm{y},\) internally in the ratio \(1: 2,\) is 

The time period of a satellite of earth is \(24\) hours. If the separation between the earth and the satellite is decreased to one fourth of the previous value, then its new time period will become \(.......\,hours\)

Both acetaldehyde and acetone (individually) undergo which of the following reactions?
A. Iodoform Reaction
B. Cannizaro Reaction
C. Aldol Condensation
D. Tollen's Test
E. Clemmensen Reduction
Choose the correct answer from the options given below:

For \(x\, \in \,R\,,\,x\, \ne \, - 1,\) if \({(1 + x)^{2016}} + x{(1 + x)^{2015}} + {x^2}{(1 + x)^{2014}} + ....{x^{2016}} = \sum\limits_{i = 0}^{2016} {{a_i\,}{\,x^i}} ,\) then \(a_{17}\) is equal to

If the area of the bounded region \(R=\left\{(x, y): \max \left\{0, \log _{e} x\right\} \leq y \leq 2^{x}, \frac{1}{2} \leq x \leq 2\right\}\) is, \(\alpha\left(\log _{e} 2\right)^{-1}+\beta\left(\log _{e} 2\right)+\gamma\), then the value of \((\alpha+\beta-2 \gamma)^{2}\) is equal to:

A shown in the figure, a battery of \(emf \;\varepsilon\) is connected to an inductor \(L\) and resistance \(R\) in series. The switch is closed at \(t=0 .\) The total charge that flows from the battery, between \(\mathrm{t}=0\) and \(\mathrm{t}=\mathrm{t}_{\mathrm{c}}\;( \mathrm{t}_{\mathrm{c}}\) is the time constant of the circuit) is